The Determinants and Consequences of Search Cost
Heterogeneity: Evidence from Local Gasoline Markets
Mitsukuni Nishiday
Marc Remerz
February 25, 2016
Abstract
Information frictions play a key role in an array of economic activities and are frequently
incorporated into formal models as search costs. However, little is known about the underlying
source of consumer search costs and how heterogeneous they are across consumers and markets.
This paper documents the sources and magnitude of heterogeneity in consumer search costs and
analyzes how the heterogeneity shapes …rms’pricing and consumers’search behavior. By identifying hundreds of geographically isolated markets, we are the …rst to estimate the distribution
of consumer search costs for many geographic markets. We directly recover the distribution of
consumer search costs market by market using retail gasoline price data in the United States.
We …nd that the distribution of consumer search costs varies signi…cantly across geographic
markets and that the distribution of household income is closely associated with the search cost
distribution. We …nd that a policy that reduces both the standard deviation and mean of the
search cost distribution has heterogeneous and potentially unintended consequences on prices
across markets.
Keywords: Search Costs, Consumer Search; Price Dispersion; Pricing; Retail Gasoline.
We have bene…ted from discussions with Tat Chan, Maqbool Dada, Babur De Los Santos, Emin M. Dinlersoz,
Anthony Dukes, Amit Gandhi, Joe Harrington, Elisabeth Honka, Han Hong, Ali Hortaçsu, Sergei Koulayev, José Luis
Moraga-González, Aviv Nevo, Zsolt Sándor, Philipp Schmidt-Dengler, Stephan Seiler, Matt Shum, Chad Syverson,
Matthijs Wildenbeest, Xiaoyong Zheng, and seminar participants at Swarthmore College, Lehigh University, Wake
Forest University, US Department of Justice, Kyoto University, Johns Hopkins University, North Carolina State
University, Osaka ISER, University of Tokyo, Center for Economic Studies at US Census Bureau, 2013 IIOC, and
the 5th workshop on consumer search and switching costs. We thank Reid Baughman, Autumn Chen, Sam Larson,
Jianhui Li, and Karry Lu for research assistance. The retail gasoline price data for this project were generously
provided by Mariano Tappata.
y
The Johns Hopkins Carey Business School, 100 International Drive Baltimore, MD 21202.
Email:
[email protected].
z
Swarthmore College, 500 College Avenue, Swarthmore, PA 19081. Email: [email protected].
1
1
Introduction
Information frictions play a key role in explaining many aspects of economic activity. Since Stigler’s
(1961) seminal article, a number of in‡uential theoretical papers, such as Varian (1980), Burdett
and Judd (1983), and Stahl (1989), demonstrate that consumer search costs can lead to competing
…rms that sell homogeneous products playing mixed strategies in price to capture sales from low
and high search cost consumers, thereby resulting in price dispersion.1 A key determinant of prices
and welfare in such models is the distribution of consumers’search costs.
Consumer search costs are not just a theoretical curiosity; …rms are often constrained by government regulations that seek to lower the cost of consumers’ search. For instance, attempting
to increase price transparency, some regulators have created online retail gasoline price aggregators that are accessible by smartphones. The purpose of such regulation is to decrease the cost
of consumer search, but it also serves to make search costs more homogeneous across consumers.
As we detail in this article, this regulation can have the unintended consequence of substantially
increasing prices and hurting consumers. Similarly, governments often regulate how gas stations
display gas prices for di¤erent payment methods (i.e., cash and credit card), which also a¤ects both
the level and variance of consumer search costs.
Despite the importance of search costs in theoretical models and its implications for …rms
and policy, we know surprisingly little about the nature of search costs and how they vary across
markets. In particular, there is little evidence documenting the determinants and consequences
of heterogeneous consumer search costs. Consequently, there still exists competing hypotheses as
to the underlying source of search costs: opportunity costs of time or search e¢ ciency (Goldman
and Johansson 1978). We …ll this gap in the literature by documenting the determinants of search
cost heterogeneity within and across markets. In doing so, we provide evidence on the underlying
source of consumer search behavior, and …nd that the opportunity cost of time is an important
factor. To perform the analysis, we structurally estimate search cost distributions for hundreds of
markets and then analyze the extent to which demographics explain the shape of the distributions.
We then conduct counterfactual experiments in each market to demonstrate how policy a¤ecting
the mean and variance of the search cost distribution impacts equilibrium prices.
The analysis proceeds in three steps. First, we document the heterogeneity of search cost
distributions both within and across retail gasoline markets. Because competition between retail
gasoline stations is highly localized, we identify 367 geographically isolated local markets in the
spirit of the …rm entry literature initiated by Bresnahan and Reiss (1991). We then structurally
estimate the search cost distribution separately for each market, and …nd that the distributions
vary signi…cantly across markets. This …nding suggests that search cost estimates from a single
market may be of limited value in making generalizable policy predictions.
Second, we explore the underlying source of consumer search costs. For this purpose, we analyze
the extent to which observable consumer characteristics can explain variation in the distribution
1
See Baye, Morgan, and Scholten (2006) for a broad review of the consumer search and price dispersion literature.
See Ratchford (2009) for a review of consumer search and pricing in the marketing literature.
2
of consumer search costs across markets. We …nd that both the mean and variance of the search
cost distribution in a market is closely related to the mean and variance of household income in a
market; these results suggest opportunity costs partly drive consumers’search costs.
Finally, using counterfactual experiments, we analyze the consequences of heterogeneity in
search costs on prices and consumer welfare. Interestingly, we …nd that a policy that decreases
both the mean and standard deviation of search costs, as would most policy aimed at increasing
price transparency, may have the unintended consequence of raising prices and decreasing consumer
welfare. On one hand, a reduction in the mean of search costs incentivizes consumers to search
more, which puts downward pressure on prices. On the other hand, a reduction in the standard
deviation reduces the fraction of (relatively) low search cost consumers, which, in turn, results in
…rms increasing market prices. We demonstrate that the latter e¤ect may dominate the former in
some markets.
This article bene…ts from extensive information on daily retail gasoline prices from almost
every station in the states of California, Florida, New Jersey, and Texas. Consumer search is
an important feature of retail gasoline markets (Marvel 1976; Chandra and Tappata 2011), and
therefore o¤ers a natural setting in which to investigate the prevalence and heterogeneity of search
costs. Other features of retail gasoline markets that are favorable to our analysis is that prices
change frequently, product characteristics are largely …xed over the sample period, and consumer
stockpiling is uncommon.
To perform the analysis, we leverage a model of …xed-sample search similar to Burdett and
Judd (1983) and directly recover the consumer search cost distribution that rationalizes observed
prices as an equilibrium outcome by …rms and consumers (Hong and Shum 2006; Wildenbeest
2011). Only price data are required to estimate search costs with this methodology, which is useful
because station-speci…c sales or indirect measures of search behavior, such as internet usage (Brown
and Goolsbee 2002), are typically unavailable for local retail gasoline markets. To rationalize search
costs from variation in retail prices, we …rst control for intertemporal variation in wholesale costs
and time-invariant price di¤erences across …rms in a market that result from vertical product
di¤erentiation. In doing so, we extend the Wildenbeest (2011) model to directly incorporate cost
shifters in a manner consistent with the theoretical model. Controlling for wholesale costs and
vertical product di¤erentiation removes 81% of observed price variation; we exploit the remaining
variation to estimate the structural model. We therefore recover the search cost distribution for
each market utilizing all intertemporal and cross-sectional variation in prices within a market,
conditional on station …xed e¤ects and wholesale costs.
We proceed as follows. The remainder of this section discusses how this article relates to the
existing literature. Section 2 describes the data and details how we choose markets within which to
perform the estimation. Section 3 presents a reduced-form analysis of price dispersion and mixed
strategies. Section 4 details the model. Section 5 presents the estimation strategy. Section 6
describes the estimation results. Section 7 conducts the counterfactual experiments and discusses
policy implications. Finally, Section 8 concludes.
3
1.1
Related Literature
This article relates to at least four strands of existing literatures. First, it is a continuation of a
recent body of research in economics and marketing that structurally estimates consumer search
costs from price data. Existing work focuses on recovering a single search cost distribution from one
product or geographic market, such as the U.S. mutual funds (Hortacsu and Syverson 2004), online
textbooks (Hong and Shum 2006), online memory chips (Moraga-González and Wildenbeest 2008),
and a chemical product (Zhang, Chan, and Xie 2015). Because these studies estimate one search
cost distribution, typically for a single market, how search costs vary across di¤erent geographies
and populations remains unknown. We, by contrast, identify hundreds of geographically isolated
markets and estimate substantial di¤erences between the search cost distributions across markets.
Appendix Table A1 compares this paper with recent work that structurally estimates search costs.
Second, our work relates to the broad literature on consumer search. Several studies, such as
Ratchford and Srinivasan (1993), Ratchford, Lee, and Talukdar (2003), Fox and Hoch (2005), Gauri,
Sudhir, and Talukdar (2008), and Brynjolfsson, Dick, and Smith (2010), focus on the consumer side
and document the marginal gains of search. We consider a model in which both consumers and
…rms optimize their choices in an equilibrium. There is also a growing literature on search costs
and competition (see, e.g., Bakos 1997; Brynjolfsson and Smith 2000; Brown and Goolsbee 2002;
Brynjolfsson, Hu, and Rahman 2009; Anderson, Fong, Simester, and Tucker 2010; Brynjolfsson, Hu,
and Simester 2011). These studies focus on the level of search costs in online marketplaces, whereas
we analyze the role of search cost heterogeneity in traditional retail markets. We complement
Kuksov (2004) and Branco, Sun, and Villas-Boas (2012), who theoretically study the impact of
lowering search costs on pricing. Moraga Gonzalez, Sándor, and Wildenbeest (2016) show through
numerical simulations how the e¤ect of …rm entry on prices depends on underlying search cost
heterogeneity within a market.
Third, this article …ts into the literature on the estimation of consumer search and considerationset formation (Roberts and Lattin 1991; Mehta, Rajiv, and Srinivasan 2003; Kim, Albuquerque,
and Bronnenberg 2010; De Los Santos, Hortacsu, and Wildenbeest 2012; Koulayev 2014; Honka
2014). Given that we only observe prices, our approach abstracts away from the decision of which
…rms to search, and instead models the size of the consideration set (i.e., how many price quotes to
obtain). In contrast to these search models of consumer demand, we estimate a model that jointly
characterizes search decisions by consumers and …rm pricing decisions, which enables us to examine
the equilibrium e¤ect of search costs on pricing.
Finally, this article relates to the literature on price dispersion, consumer search, and pricing in
retail gasoline markets. A number of studies, such as Marvel (1976), Barron, Taylor, and Umbeck
(2004), Lewis (2008), Lewis and Marvel (2011), Chandra and Tappata (2011), and Pennerstorfer,
Schmidt-Dengler, Schutz, Weiss, and Yontcheva (2015), have identi…ed patterns of temporal and
cross-sectional price dispersion in retail gasoline markets that are consistent with models of costly
consumer search. Because search costs are not directly observed in these studies, the evidence
has been limited to carefully executed reduced-form testing of comparative static relationships
4
implied by a particular theoretical model. By contrast, we structurally back out the search cost
distributions that rationalize the model and observed data. We contribute to the literature that
examines more generally the pricing of retail gasoline. Firgo, Pennerstorfer, and Weiss (2015)
estimate the pricing power a¤orded to retail gasoline stations that are centrally located in a network.
Chan, Padmanabhan, and Seetharaman (2007) propose an empirical model of pricing and location
decisions of gas retailers in Singapore. Iyer and Seetharaman (2003) examine price discrimination
in the Greater St. Louis retail gasoline area. Using a model of product and pricing decisions, Iyer
and Seetharaman (2008) investigate why some markets observe similar gas prices and other markets
do not. We contribute to this literature by better understanding the role that search frictions play
in retail gasoline pricing.
2
The Data
2.1
Price and Wholesale Cost Data
We utilize a large panel data set of daily, regular fuel gasoline prices for individual gas stations. The
data originate from the Oil Price Information Service (OPIS), which obtains data either directly
from gas stations or indirectly from credit card transactions. Academic studies of the retail gasoline
industry have frequently relied upon OPIS’s data (e.g., Lewis and Noel 2011; Taylor, Kreisle, and
Zimmerman 2010; Chandra and Tappata 2011). Using a subset of the price data employed in
Chandra and Tappata (2011), we estimate the model with data from gas stations in California,
Florida, New Jersey, and Texas from February 27 through March 28, 2007. We refer interested
readers to Chandra and Tappata (2011) for a more detailed description of the data.
The structural model requires only price data, and reconciles the observed price dispersion as
a consequence of vertical product di¤erentiation and heterogeneity in consumers’ cost of search.
In the full set of price data, which spans January 4th, 2006 through May 16th, 2007, prices may
vary over time, in part, in response to changes in the wholesale cost of gasoline. To minimize
the impact of input cost changes on observed price dispersion, we incorporate the spot price of
wholesale gasoline directly into the empirical analysis and use only the 30 consecutive days of data
that minimize variation in wholesale costs.
We utilize the spot price of wholesale gasoline traded on the New York Mercantile Exchange
(NYMEX) as the measure of wholesale costs. These data are commonly employed as a measure
of marginal cost in studies of the retail gasoline industry (e.g., Borenstein, Cameron, and Gilbert
1997; Velinda 2008; Lewis 2011). February 27th through March 28th, 2007 are the dates that
minimize wholesale cost variation; the standard deviation of the daily New York Harbor spot price
of wholesale unleaded fuel was 6.3 cents per gallon over that time. To address regional di¤erences
in wholesale prices, we use the daily spot price of reformulated gasoline delivered to the New York
Harbor, Gulf Coast, and Los Angeles2 for gas stations located in those respective regions. To
2
These prices are available publicly through the U.S. Energy Information Administration (eia.gov). City-level rack
wholesale prices are likely a more accurate measure of marginal cost, but such data are proprietary.
5
further account for marginal cost movement creating price dispersion in the data, we estimate the
model using a …rm’s markup of price over wholesale cost (p
c) rather than its price. Section 5
develops how using markups rather than prices is consistent with the theoretical model. Estimation
results are qualitatively similar whether the model is estimated using prices or markups, likely due
to a priori selecting a time period with minimal wholesale cost variation.
2.2
Location Data and Selecting Isolated Markets
In the structural model, prices are generated by an equilibrium in which a de…ned set of gas stations
compete for the same set of customers. Markets in the data must therefore be carefully de…ned
to be consistent with this assumption. In retail gasoline markets, competition among stations is
highly localized (Eckert 2013), and typically the literature de…nes a market as a speci…ed radius
around each …rm in the data (see, e.g., Hastings 2004; Barron, Taylor, and Umbeck 2004; Lewis
2008; Remer 2015). A potential source of estimation bias inherent in this market de…nition is the
existence of overlapping markets; two …rms within a speci…ed distance that compete against each
other may belong to multiple markets, but each …rm may not belong to the same total sets of
markets.
To circumvent this problem, we focus the analysis on “isolated” markets, which we de…ne in
the spirit of Bresnahan and Reiss’s (1991) geographic markets. We use two strict criteria. First,
we de…ne an isolated market as a set of …rms all within 1:5 miles of each other, and no other
competitor is within 1:5 miles of any …rm in the market. Formally, let J be a set of …rms and let
d(i; j) be the distance between any two …rms i; j 2 J. Then, J is an isolated market if (a) for all
i; j 2 J, d(i; j)
X, and (b) for all k 2
= J and i 2 J, d(i; k) > X. We choose 1:5 miles as the
maximum distance between …rms in a market (X), which is consistent with Barron, Taylor, and
Umbeck (2004), Hosken, McMillan, and Taylor (2008), and Lewis (2008). Restricting the analysis to
isolated markets ensures that prices in a market are not in‡uenced by competition with unobserved
competitors, and therefore stands as an improvement over previous literature that allows …rms to
belong to multiple overlapping markets. Nonetheless, Moraga-González and Wildenbeest (2008)
do …nd that the estimation methodology employed in this article may be robust to missing data
entirely from some …rms in the market. To implement the isolated market de…nition, we converted
the street address of each gas station to longitude and latitude coordinates using ArcGIS, and then
cross-referenced them with coordinates outputted from Yahoo maps, and …nally, we calculated the
geodesic distance between each pair of gas stations.
Second, to analyze the relationship between search costs and census tract-level characteristics,
we further restrict isolated markets to only include markets where all gas stations are located
within a single census tract.3 Figure 1a depicts a map containing an isolated market with two …rms
within a single census tract (“Market 1”). Using only isolated markets, we estimate the model
using prices from 1; 145 stations in 367 isolated (and single census tract) markets. Figure 1b shows
3
Manuszak and Moul (2009) use a census tract as the unit of observation to analyze the relationship between
consumer heterogeneity and travel costs in retail gasoline markets.
6
the distribution of these markets by the number of gas stations. De…ning isolated markets does
not solve all potential issues; for example, people may purchase gasoline not only where they live,
but also along their commute to work. Still, the isolated market de…nition is more stringent than
those used by most of the existing literature. A notable exception is Houde (2012), who directly
incorporates information on commuting routes in the Quebec City gasoline market.
[Insert Figures 1a and 1b about here.]
Table 1 presents census tract population summary statistics for isolated markets and the remaining non-isolated markets in the data; the structural estimation of consumer search costs in
isolated markets incorporates this data. The data are taken from the 2006-2010 American Community Survey (ACS), an ongoing survey conducted under the auspices of the US Census Bureau.
Mean income and age are taken directly from the survey, while mean years of education are calculated by taking a weighted average of the people in a census tract who have reached a particular
educational attainment. The ACS reports the number of households that fall within a particular
income bracket; by assuming that average household income within a bracket is the mid-point of
the bracket, we calculate the standard deviation of income.
[Insert Table 1 about here.]
Table 1 demonstrates that isolated and non-isolated markets are similar in terms of income,
education, and age, suggesting the subsequent results are generalizable to other markets. The only
substantive di¤erence between isolated and non-isolated markets is that gas stations tend to be
closer together in isolated markets. This is because we restrict isolated markets to have stations
that fall within a single census tract, which tend to be smaller than a circle of 1.5 mile radius.
3
Evidence of Price Dispersion
3.1
Reduced-form Evidence
A large body of economic literature documents price dispersion in retail gasoline markets, and our
data are no exception. The isolated markets in the data are characterized by substantial price
dispersion, which is summarized in Table 2. The …rst column of Table 2 pools the prices across
all isolated markets and 30 days of data from February 27 through March 28, 2007, and presents
summary statistics for the distribution of all prices in the data. Column 2 presents the same
for markups of price over wholesale costs.4 The average price (markup) in the data we use to
estimate search costs is $3:12 ($0:76) and the range (i.e., maximum minus minimum price) and
standard deviation of all prices (markups) is $1:00 and $:099 ($1:03 and $:089), respectively. To
facilitate comparison of prices across states, state …xed e¤ects are removed from the prices, which
4
When we estimate the structural model using markups rather than prices the estimates converge in 13 more
markets (367 vs. 354). We present summary statistics only for markets where we obtain estimates, and therefore
columns 2 and 4 have more observations.
7
largely controls for state taxes. It is of note that the price and markup distributions have a very
similar range and standard deviation. If price dispersion were largely a consequence of wholesale
price movement, retail prices would be much more dispersed than markups. In the extreme, if
gas stations set price as a …xed markup over cost then we would observe price dispersion, but no
variation in markups.
[Insert Table 2 about here.]
Columns 3 and 4 in Table 2 characterize the distribution of prices and markups, respectively,
within isolated markets and provide evidence on how the distributions vary across markets. For
each statistic, such as the mean retail price, we …rst calculate the statistic within a market, and
then take the average of it across all isolated markets. For example, on average across markets, the
mean price within a market for all 30 days of data is $3:12 and the standard deviation of the mean
price across markets is $0:07. The average range and standard deviation of prices across markets
are only slightly larger than those of markups, again suggesting that wholesale cost changes are not
a major determinant of price dispersion in our data. This …nding is likely due to selecting a time
of minimal wholesale cost movement, as, in general, wholesale gasoline prices change over time and
are an important determinant of retail gasoline price movement.
Figures 2a and 2b compare the distribution of all prices and markups to the distributions
within three isolated markets, each with three gas stations. The …rst panel of Figure 2a depicts
the distribution of all observed prices in isolated markets. The distribution of all prices has a
much larger range and variance than the price distributions depicted for three individual markets.
This pattern demonstrates that there are important di¤erences in the distributions of prices across
markets. It is also interesting that the markup distributions appear smoother than their price
counterparts, perhaps suggesting that the markup speci…cation is more appropriate for estimating
search costs.
[Insert Figures 2a and 2b about here.]
Figures 3a and 3b more fully characterize the heterogeneity of price distributions across markets.
Figure 3a depicts histograms of the mean and standard deviation of prices in each isolated market,
and Figure 3b presents a scatter plot of the standard deviation of prices against the mean market
price. As in Table 2, mean market prices are net of state …xed e¤ects. The histogram of standard
deviations illustrates that there is a mass of markets wherein the standard deviation of prices is
about 5-6 cents per gallon, and the distribution is skewed right. The histogram of average prices
also shows substantial variability in average market prices, which range from just under $3:00 to
more than $3:30. In total, there appears to be a substantial degree of heterogeneity in both the
mean and standard deviation in prices across markets.
[Insert Figures 3a and 3b about here.]
8
Interestingly, Figure 3b demonstrates, and simple regressions con…rm, that in general there is
no meaningful relationship between price levels and the standard deviation of prices. This result
highlights the degree of heterogeneity in price distributions across the isolated markets. As the
structural model maps the observed distribution of price-cost markups into the distribution of
consumer search costs, these …gures suggest that the estimation will yield meaningful di¤erences in
search cost distributions across markets.
In the structural model presented below, the mapping from the consumer search cost distribution
to the equilibrium price distribution is non-linear. For example, as shown in Chandra and Tappata’s
(2011) …xed-sample search model, there is no price dispersion when the search costs are very
low or high, because the former leads to competitive pricing and the latter leads to monopoly
pricing. At intermediate search costs price dispersion exists. Taken as a whole, this implies a nonmonotonic relationship between the moments of the search cost and price distributions. Appendix
A1 demonstrates the same property in the model we estimate. It follows that studies that relate
simple proxies for consumer search costs, such as the distance between stations or the number of
commuters, to measures of price dispersion may be limited in testing how changes in the cost of
search a¤ect prices. Also, the complex relationship between price and search distributions implies
that simple measures of price dispersion may poorly proxy for the search cost distribution in
identifying the relationship between search costs and market characteristics.
[Insert Table 3 about here.]
To underscore this point, the results of regressing di¤erent measures of price dispersion on market and population characteristics are presented in Table 3, and we …nd that the signi…cance of
regressors is sensitive to how price dispersion is measured. For example, mean and log-mean income
are positively and signi…cantly correlated with the sample range of prices in the second, third, and
fourth speci…cations, but are not signi…cantly related to the sample standard deviation of prices.
The signi…cance of other variables, such as the average distance among stations and the log of education, is also sensitive to how price dispersion is measured. Furthermore, all speci…cations in the
regressions fail to …nd a correlation between the standard deviation of income and price dispersion.
This reduced-form result may not be surprising, because, as developed in Chandra and Tappata
(2011), the equilibrium relationship between price dispersion and consumer search costs is theoretically non-monotonic. In the structural analysis that takes into account this non-monotonicity, we
…nd a robust connection between the standard deviation of income and the variance of consumer
search costs. It therefore appears that the distribution of prices is, at best, an imperfect proxy for
the distribution of search costs.
Finally, we analyze the extent to which cross-sectional and temporal price variation is explained
by di¤erences across gas stations and wholesale cost changes. To do so, we run simple regressions
of prices on wholesale costs and …rm …xed e¤ects. Using data from all stations and dates in the
data set, column 1 in Appendix Table A2 shows station …xed-e¤ects explain 30% of the variation in
prices. Column 2 shows that adding wholesale prices increases the r-squared to :81, suggesting that
9
much of the price dispersion in retail gasoline markets may be explained by marginal cost changes
and station characteristics. Restricting the data to only stations in isolated markets and the 30-day
time window for which we estimate search costs, we …nd that station …xed e¤ects and wholesale
costs explain 96% of the price variation. Thus, search costs likely explain at most between 4% and
19% of observed price dispersion.
When using all of the data and including …rm …xed e¤ects (column 2), we estimate a coe¢ cient
of 0:89 on wholesale costs. Previous studies of retail gasoline markets have estimated the coe¢ cient
to be one (Remer 2015; Bachmeier and Gri¢ n 2003; Borenstein et al. 1997). Furthermore, industry
reports …nd that oil and re…ning account for almost 80% of retail fuel costs and the accounting
margins are typically slim.5 Thus, it would be unpro…table in the long-run for gas stations to
maintain a wholesale cost pass-through rate below 1. To construct the markup variable in the
structural estimation, we e¤ectively assume that the wholesale coe¢ cient is equal to one, which is
consistent with previous empirical …ndings and industry reporting.
3.2
Evidence of Mixed-Strategies
A large body of empirical literature analyzing retail gasoline markets documents price dispersion as
a consequence of gas stations playing mixed strategies to extract informational rents from consumers
with search costs (e.g., Lewis 2008; Hosken et al. 2008; Chandra and Tappata 2011; Lach and
Moraga-Gonzalez 2012). Using much of the same data as in this article, Chandra and Tappata
(2011) demonstrate that retail gasoline price dispersion can be explained by a model where …rms
use mixed strategy pricing. As evidence of price dispersion and mixed strategies, Chandra and
Tappata (2011) calculate rank-reversal statistics by computing the percentage of days the typically
lower-priced …rm sets a higher price, and show that pairs of closely located gas stations often switch
between which sets a higher price. Hosken et al. (2008) and Lewis (2008) similarly …nd that gas
stations often switch places in the market price distribution.
We subset the data used in Chandra and Tappata (2011) into isolated markets and use a
narrower time frame, and …nd similar evidence of mixed strategies. First, we replicate the rankreversal analysis. Appendix Table A3 shows that there are a mass of …rms which never switch price
rankings, and on average the low-price …rm sets a high price 8:2% of days. As we detail in the model
below, due to vertical product di¤erentiation, competing …rms may play mixed strategies but, due
to quality di¤erences, draw prices from non-overlapping price distributions; such …rms would never
reverse price rankings. For the set of …rms with positive rank-reversals, the rank-reversal statistic
is distributed almost uniformly between zero and 50%. In theory rank-reversals could be generated
from Edgeworth price cycles, which have been observed in gasoline markets (Noel 2007; Lewis and
Noel 2011); however, we …nd no evidence of Edgeworth price-cycles in any of the markets included
in the analysis.
5
These
numbers
are
reported
by
the
Association
for
Convenience
&
Fuel
Retailing
(www.nacsonline.com/YourBusiness/FuelsReports/2015/Prices/Pages/The-Price-Per-Gallon.aspx). Last accessed
December 2015.
10
In the structural model, …rms compete by playing mixed strategies in utility, rather than in
prices, and utility is empirically identi…ed by removing a …rm …xed e¤ect and wholesale price. As
such, we calculate utility rank-reversals for …rms in isolated markets and …nd more support for
mixed strategies. We …nd that the low-utility …rm, on average, sets the higher utility on 25% of
days. Furthermore, …rms e¤ectively never o¤er the same utility on a particular day; we …nd ties in
utility on only 0:4% of days, which further evidences …rms playing mixed strategies in utility space.
We …nd that two …rms in an isolated market o¤er the same retail price on 28% of days.
Finally, we analyze whether prices, and therefore utility, exhibit autocorrelation, which would
be evidence against mixed strategies. Appendix Table A4 shows that when pooling prices from
the 367 markets for which we estimate search costs, we fail to reject the null hypothesis of no
autocorrelation with even 90% con…dence. Taken as a whole, we believe the evidence supports gas
stations in our data playing mixed strategies, which is consistent with many previous studies of
retail gasoline markets.
4
A Model of Consumer Search with Vertical Product Di¤erentiation
We introduce a …xed-sample search model based on the presentation in Hong and Shum (2006) and
Wildenbeest (2011).6 The empirical …xed-sample search model developed in Wildenbeest (2011)
modi…es Burdett and Judd (1983)’s theoretical model in two ways; the number of …rms is discretized
and vertical product di¤erentiation is incorporated. We …rst introduce several assumptions on
consumers’and …rms’behavior, and then discuss optimality conditions for both.
We consider N gas stations (“…rms”) selling a vertically di¤erentiated product to a continuum of
consumers. Consumers have inelastic demand for one unit of gasoline, and are identical except for
their search costs. Consumers draw an i.i.d. search cost, c
0, from the cumulative distribution, Fc .
Firms do not observe an individual consumer’s search cost, but know the cumulative distribution
of search costs.
Consumers have the same preferences over quality, which makes products vertically di¤erentiated. The utility from purchasing from station j is given as follows:
uj = vj (wj )
pj :
(1)
Here, uj is the utility of purchasing from …rm j at a price of pj . The value consumers obtain
from a …rm of quality wj takes the following form, vj (wj ) = x + wj , where x can be thought of
as the minimum quality across …rms and additional quality, wj , enters additively and separably.
Consumers know a priori vj , which is constant over time, but do not observe pj , and hence the
utility …rm j will provide unless that station is searched for its price.
We make two assumptions about …rms’ production: quality inputs are purchased in per6
Appendix A3 discusses …xed-sample versus sequential search.
11
fectly competitive markets, and the quality production function exhibits constant returns to scale.
Perfectly competitive input markets imply that quality inputs are paid their marginal product.
Constant returns to scale imply that …rms choose wj to maximize the valuation-cost markup,
vj (wj )
r(wj ), where r(wj ) is the marginal cost of o¤ering a product of quality wj . From these
two assumptions and Euler’s theorem, it follows that the cost of obtaining a given level of quality
is simply r(wj ) = wj , and the value provided by a …rm can be denoted as:
vj = x + rj :
Given equations (1) and (2), …rm j’s pro…t margin is pj
(2)
rj = (vj
uj )
rj = x
uj , which implies
…rm j chooses uj to maximize its pro…t margin. As such, the relevant strategy space for …rms can
be formulated in terms of utility rather than prices, and we can focus on mixed strategies in utility.
In equilibrium, …rm j varies its utility over time by changing pj such that any systematic di¤erence
in prices relative to other stations, E[pj
and thereby rj
r
j.
p
j ],
exactly re‡ects the di¤erence in its value, vj
v
j,
Because the marginal costs re‡ect di¤erences in quality, all …rms earn the
same expected pro…ts, even under vertical product di¤erentiation. Firms are therefore symmetric
in the utility strategy space, and we focus on symmetric equilibria.
As …rms di¤er in quality, in order to provide the same expected utility, a higher quality …rm
will tend to set a higher price. The equilibrium generates a utility distribution, Fu (u), that is i.i.d.
across stations; u and u are the lower and upper bound, respectively, of the support of Fu .
¯
In equilibrium, consumers know the distribution of utility, Fu (u), but must engage in costly
search to learn the price, and thereby utility, o¤ered by a particular …rm. Consumers receive one
free price quote and then pay a cost, c, for each additional quote. Consumers do not observe any
prices before choosing the number of searches that maximize expected utility, which consists of uj
minus the total cost of search. Consumers purchase from the …rm in its sample that o¤ers the
highest utility.
A consumer’s problem is to maximize overall expected utility by choosing the number of quotes,
l:
l = arg max c (l
l 1
The …rst term,
1) +
Z
u
l u Fu (u)l
1
f (u)du:
u
¯
c (l 1); is the total cost of actively searching l 1 stations. The second term is
the expected utility from consumption when a consumer has l quotes, and Fu (u)l
1
is the probability
that l 1 …rms o¤er utility lower than u. By searching l+1 rather than l …rms, a consumer obtains an
expected marginal bene…t, which is denoted as
l
Eu1:l+1
Eu1:l , l = 1; 2; :::; N
1. Here, Eu1:l
represents the maximum expected utility when a consumer takes l draws from Fu . Accordingly, a
consumer with search cost c will sample l stores when
l 1
>c>
l.
A consumer with c =
l
is
indi¤erent between searching l and l + 1 …rms. The proportion of consumers with l utility quotes,
ql , will be q1
1
Fc (
1)
for l = 1, and ql
Fc (
l 1)
total market demand from consumers that actively search l
12
Fc (
l)
for l
2. Therefore, ql is the
1 …rms prior to purchasing.
Given consumers’optimal search behavior, each …rm chooses a symmetric mixed-pricing strategy, Fu , for all u 2 [u; u] to maximize pro…ts. In a symmetric equilibrium, all utility in the support
¯
of Fu generates the same expected pro…t, and therefore a …rm is indi¤erent between o¤ering the
lowest utility u and any other utility u 2 [u; u]. Firm j’s total pro…t can then be denoted as
¯ P
¯
l
l 1 ]. The highest price …rm j may set is p = v , and therefore
uj )[ N
j (u) = (x
j
j
l=1 ql N (Fu (uj )
o¤ers no utility, uj = vj pj = 0. In this case, …rm j attracts only consumers with one price quote,
¯
and its pro…t will be j (u) = Nx q1 . Accordingly, we can represent the indi¤erence equilibrium
¯
condition for …rms as:
(u) = x
q1
= (x
N
N
X
u)[
ql
l=1
l
Fu (u)l
N
1
], for u 2 [u; u]:
¯
(3)
The equal pro…t condition in equation (3) does not have a closed-form solution in Fu . As we detail
in the next section, however, points on the distribution can be identi…ed. Note that this condition
does not depend on market size, as consumers have an inelastic demand for one unit and therefore
pro…ts are perfectly linear in market size. Thus, variation across markets in time-invariant demandside characteristics, such as income and population, will only a¤ect the mixed strategy equilibrium,
and therefore price dispersion, indirectly through the distribution of search costs. Equation (3) can
be solved implicitly for utility as:
PN
l=2
u = x PN
lql Fu (u)l
1
l 1
l=1 lql Fu (u)
:
(4)
Finally, given the equilibrium utility distribution, Fu (u), and valuation at the …rm level, vj , we can
recover the price distribution for …rm j, Fj (p), as
Fj (p) = Pr[pj
5
5.1
p] = Pr[p
vj
uj ] = Pr[uj
vj
p] = 1
Fu (vj
p):
(5)
Estimation Strategy
First Stage: Identi…cation and Nonparametric Estimation of Search Costs
at the Market Level
The …rst-stage estimation strategy extends Moraga-González and Wildenbeest (2008) and Wildenbeest (2011) to control for intertemporal price dispersion that arises from changes in production
cost. The Hong and Shum (2006) framework recovers the distribution of consumer search costs
using only price data by rationalizing all observed price dispersion as a consequence of search costs.
Also relying solely only price data, Wildenbeest (2011) converts prices to utility by controlling for
vertical product di¤erentiation with …rm-speci…c …xed e¤ects, and then maps the dispersion in utility onto the distribution of search costs. Controlling for vertical product di¤erentiation is important
in the retail gasoline industry; within a market …rms may vary in the quality of service, location,
and brand. Previous research, such as Lewis (2008), demonstrates that these characteristics are
13
…xed over time and explain a substantial degree of price dispersion. We extend Wildenbeest (2011)
to incorporate data on wholesale costs, which allows us to control for price variation that results
from changes in marginal costs. This change stands as an improvement over previous structural
estimates of consumer search costs, which map all price dispersion remaining after controlling for
vertical product di¤erentiation onto the distribution of search costs. We apply this methodology
separately to each geographically isolated retail gasoline market. We treat price observations as
independent across days and stations after controlling for station …xed e¤ects and wholesale costs.
We …nd in Section 3 that prices, and therefore utilities, are not autocorrelated, which supports this
treatment.
To estimate the model, we …rst use the price and wholesale cost data to estimate the utility
provided by a gas station on a particular day. To do so, we follow Wildenbeest (2011) and solve
equation (1) for price and add a time subscript: pjt = vjt
ujt . To control for changes in wholesale
costs, we assume that the unit cost at the …rm level takes the form rjt = r + ct +
j,
where r is a
time-invariant component of marginal cost that is common across …rms, ct is a time-varying cost
component shared by all …rms, such as wholesale prices, and
j
varies with …rms’ quality, but is
…xed over time. Equation (2) gives vjt = x+rjt = x+r +ct + j , and plugging vjt into pjt = vjt ujt
yields:
pjt = x + r + ct +
ujt :
j
To identify utility, we estimate the following equation via …xed-e¤ect regression:
pjt
ct = x + r +
=
where
= x + r is a constant term,
j
+
j
+
j
+
jt
jt ;
is a …rm-speci…c …xed e¤ect, and
(6)
jt
is an idiosyncratic
shock. We construct the markup of price over wholesale cost by subtracting the wholesale price
data from a …rm’s retail price. We then recover the utility o¤ered by station j at time t by running
the …xed-e¤ect regression and setting u
^jt = (pjt ct ) + ^ + ^j = ^jt . Therefore, the utility
o¤ered by a …rm at a point in time is identi…ed as the negative of the residual in equation (6). The
systematic di¤erences in …rms’markups are attributed to di¤erences in the …rms’product quality.
With these estimates in hand, we identify the model parameters using the variation in utilities
over time and across …rms. Formally, we utilize the equilibrium condition speci…ed in equation (3),
and conduct nonparametric estimation of this optimality condition. The estimation methodology
follows Moraga-González and Wildenbeest (2008), who extend Hong and Shum (2006) through the
maximum likelihood estimation (MLE) approach to achieve more favorable convergence properties.
Denoting the number of gas stations in a market by N and the number of price observations in that
market by I, we employ the MLE to estimate the model parameters ^M LE = f^
ql gN 1 such that:
l=1
I 1
^M LE = arg max P log fu (ui ; q1 ; ::; qN );
1
fql gN
l=1 i=2
14
where fu is the density function of Fu . Following Wildenbeest (2011), we apply the implicit function
theorem to equation (3) to yield the density for equilibrium utility:
N
P
fu (ui ) =
(x
lql (Fu (ui ))l
l=1
N
P
ui )
1
,
l(l
1)ql (Fu (ui
(7)
))l 2
l=1
where Fu (ui ) solves equation (3) for i = 1; ::; I. Because all …rms draw utility from the same
equilibrium distribution, Fu , we pool all estimated utilities in a market to estimate the model
parameters. The maximum likelihood routine yields parameter estimates that can be used to
construct points on the non-parametric search cost CDF, f ^ l ; F ( ^ l )g. These estimates have the
asymptotic properties of standard maximum likelihood estimation, and we compute the standard
errors accordingly.
Identi…cation of the …rst-stage model. To identify the model’s primitives, we utilize the
restrictions imposed by the theoretical model to map dispersion in utilities onto the distribution
of consumer search costs. Intuitively, we proceed in two steps. First, we subtract wholesale costs
from prices to control for intertemporal price dispersion due to marginal cost changes. Using
the markups of price over wholesale cost, we then exploit the cross-sectional variation in markups
across stations within a market to identify the …rm-speci…c …xed e¤ect
j,
which controls for vertical
product di¤erentiation. By subtracting the estimated …xed e¤ect from the markup, we recover the
utility provided by station j at time t, which is then used in the MLE routine.7 Second, by
assuming …rms play a mixed strategy in utility, the intertemporal variation in utility within a …rm
and cross-sectional variation in utility across …rms identi…es the remaining structural parameters
of the …rst-stage model through the equilibrium restrictions in equation (3).
More formally, for a market with N stations and I price observations, there are N 1 unknown
PN 1
parameters in the model fq1 ; q2 ; ::; qN 1 g, where qN = 1
l=1 ql : Using the station-level …xed-
e¤ect regressions in equation (6), we identify for each price observation the implied utility u
^ as the
residuals from the regression multiplied by 1, which we use to construct the empirical distribution
of utility F^u (u) through equation (5). Then, using the empirical distribution of utility, we identify
1
^l
the marginal utility of search, f ^ l gN
l=1 , such that
Eu
^1:l . We then set u’ and u0
¯
to be the lowest and highest observed utility, and then order the I utility estimates: u’= u
^1 u
^2
¯
0
::: u
^I = u . The empirical counterpart of the …rms’indi¤erence condition is:
q^1
x
^
= (^
x
N
N
X
u
^i )[
q^l
l=1
l ^
Fu (ui )l
N
Eu
^1:l+1
1
]; i = 1; 2; ::; I:
(8)
Applying the implicit function theorem to this equation yields the likelihood function, equation
7
Because of the station …xed e¤ect in equation (6), the empirical model does not rely on systematic di¤erences in
prices across stations within a given market.
15
(7), and I
1 corresponding moment restrictions implied by the model equilibrium. Accordingly,
for all markets such that I
1
N
1, we identify the model parameters, f^
q1 ; q^2 ; ::; q^N 1 g, and
the corresponding non-parametric cumulative distribution of search costs: Fc ( ^ l ) = Fc ( ^ l 1 ) q^l .
We then evaluate the empirical indi¤erence condition in equation (8) at the highest utility u to
identify the time-invariant and common component of the valuation-cost margin:
PN
l=1
x
^ = u PN
q^l l
^l
l=2 q
l
:
(9)
The lower bound of the utility distribution, F (u), is normalized to zero; a station o¤ering zero
utility will only sell to consumers with one price quote, and the station maximizes pro…t by setting
the maximum price pj = vj , such that u= 0. We then compute the maximum utility u by solving
¯
for Fu (u) = 1 in equation (4).
5.2
Second Stage: Estimation of Parametric Search Cost Distribution That
Allows for Variation Across Markets
The …rst stage estimation routine produces estimates of points on the distribution of search costs
separately for individual isolated markets. We use these estimates to understand how the distribution of search costs relate to observable market and consumer characteristics. To achieve this goal,
we pool the estimated points of the search cost CDFs across all markets, and use nonlinear leastsquares (NLS) regression to …t a parametric distribution. Following previous work, including Hong
and Shum (2006), Chen, Hong, and Shum (2007), and Wildenbeest (2011), we use the log-normal
distribution as the main speci…cation. As a robustness check, we also …t a normal distribution.
Given the …rst stage search cost estimates, f ^ l;m ; q^l;m gN 1 in each market, m, we employ NLS
l=1
to estimate the log-normal parameters, ( ; ), using the following equations,
y^l;m =
1
^ l;m
m
= Xm
m
= Xm
y^1;m = 1
m
p
2
e
(ln( ^ l;m )
2
2 m
q^1;m ; y^2;m = 1
2
m)
q^1;m
for l = 1; ::; N
q^2;m ; :::; y^N
1;m
=1
1; where,
N
X1
q^l;m
l=1
In the regression, the mean and variance parameters,
and , respectively, depend upon market-
level characteristics, Xm and Xm . The cross-sectional variation in search cost distributions across
markets allows us to identify the second stage parameters. These parameters describe how market characteristics in‡uence the mean and variance of the consumer search cost distribution, and
therefore are informative about the underlying cause of consumer search behavior.8
8
We assume that the intertemporal and cross-sectional variation in prices, after removing wholesale cost variation
and station …xed e¤ects, is generated by …rms’ mixed strategy given the search cost distribution. In Appendix
16
6
Estimation Results
6.1
Search Cost Estimates
We estimate the proportion of consumers that search l stations, q^l , and a combination of points,
f ^ l ; F^c ( ^ l )g, on the search cost CDF for each of 367 markets. Table 4 summarizes the estimates
of q^l and ^ l , and the per-gallon valuation-cost margin per gallon, x
^, across isolated markets. We
…nd that there is not much consumer search in retail gasoline markets; across markets, on average,
66:4% of consumers receive only one price quote. These consumers visit only one gas station,
and therefore do no price comparison shopping before purchasing. The average marginal expected
savings from visiting a second station is $0:032 per gallon. While the average search intensity is low,
there is substantial heterogeneity across markets; the standard deviation of q^1 is 0:155. Moreover,
its range is 0:936
0:004 = 0:932; therefore in at least one market almost all consumers search and
in another no one searches.
[Insert Table 4 about here.]
To illustrate how search cost distributions vary across markets, we randomly pick …ve markets
in Texas that have three stations. Figure 4a plots ( ^ 1 ; Fc ( ^ 1 )) and ( ^ 2 ; Fc ( ^ 2 )) for each market,
and the …gure displays substantial di¤erences between the distributions. For instance, the fraction
of non-searchers (q1 = 1 Fc ( ^ 1 )) in market 1 is 0:09, and the gain from the …rst search is $0:02
(= ^ 1 ) per gallon of regular gasoline. In market 4, on the other hand, the fraction of non-searchers
is 0:89, and the gain from the …rst search is $0:04 (= ^ 1 ) per gallon. Thus, for similar marginal
savings, there is a wide disparity between these two markets in the propensity to engage in costly
search, indicating that there is a large di¤erence in consumer search costs.
[Insert Figures 4a and 4b about here.]
Finally, the valuation-cost margin parameter, x, and price distributions implied by the model
are well estimated. The estimated maximum valuation-cost markup is on average $0:261 per gallon
across markets. Appendix Figure A1 displays the distribution of estimated valuation-cost margin
for duopoly markets (Figure A1a) and markets with more than two …rms (Figure A1b). We …nd that
the valuation-cost margins are skewed to the right for both markets. Furthermore, the equilibrium
price distribution from the estimated model approximates the empirical distribution of prices in
most markets. For instance, Figure 4b presents the empirical and estimated price distribution from
a market in Florida.
A2, we assess the possibility that time-invariant, market-level characteristics a¤ect intertemporal variation through
means other than search costs; we do not …nd evidence that these characteristics directly and meaningfully a¤ect
intertemporal pricing.
17
6.2
Estimation of Parametric Search Cost Distribution That Allows for Variation Across Markets
This subsection sheds light on the underlying source of search costs. Our aim is to determine the
extent to which (i) the mean and variance of search cost distributions vary across markets and (ii)
this variation can be explained by observable market and population characteristics.
Heterogeneity of search costs. Table 5 presents the results of pooling the …rst stage search
N 1
cost estimates, f ^ l;m ; q^l;m gl=1
, from all m = 366 markets,9 and using nonlinear least-squares to
…t a log-normal (columns 1 through 3) and normal (column 4) CDF. The log-normal speci…cations
(columns 1 through 3) deliver lower mean squared residuals than the normal distribution speci…cation (column 4). We regard column 1 as the baseline speci…cation, and columns 2 and 3 examine
whether the results are robust to the exclusion of imprecisely estimated parameters.
[Insert Table 5 about here.]
Using the estimates from column 1, we predict for each market the mean and variance of the
search cost distribution, and present the distribution of results in Figures 5a and 5b. In Figure
5a, the histogram of mean search costs is skewed to the right and exhibits heterogeneity across
markets around the median of $0:127 per gallon. Interestingly, the histogram of mean market
prices presented in Figure 3a exhibits very little skewness, again reinforcing that price distributions
are not a perfect proxy for search cost distributions. Figure 5b similarly demonstrates substantial
heterogeneity in the variance of search costs across markets.
[Insert Figures 5a and 5b about here.]
To quantify the degree of heterogeneity, we compare percentiles within the distributions presented in Figures 5a (distribution of estimated means) and 5b (distribution of estimated standard
deviations). The 75-25 and 90-10 percentile ratios of the estimated means are 1:630 and 2:572,
respectively. Similarly, the 75-25 and 90-10 percentile ratios of the estimated standard deviations
are 2:109 and 4:695, respectively. These ratios con…rm a great amount of variation in search cost
distributions across markets, and suggests caution when generalizing search cost estimates from a
single geographic market to other markets.
Potential sources of search cost heterogeneity.
Having established the presence of het-
erogeneity in search cost distributions, we now investigate the source of consumer search costs.
While the empirical model in the …rst stage is agnostic as to the underlying source of search costs,
the second-stage estimation is designed to shed light on the potential causes. Following Goldman
and Johansson (1978), we argue that search costs may derive from the (1) cost of information acquisition, such as opportunity cost of time and other expenditures (e.g., driving, phone calls, internet
9
We exclude one market from the second stage estimation because it was missing demographic variables included
as controls in the NLS regression.
18
access, etc.), which may vary with household income, and (2) information-processing or cognitive
costs, which may vary with education or age. Note that these two sources of consumer search costs
are not mutually exclusive. For example, online price search likely possesses both components;
it requires time in front of a computer (cost of information acquisition) and knowledge of which
websites to search and which gas stations are located near the desired commuting path (information processing costs). During the sample time period, 2007, retail gasoline search was a mixture
of online and o- ine; websites such as gasbuddy.com, mapquest.gasprices.com, and autos.msn.com
listed prices for individual gas stations searchable by zip code.
The results in Table 5 demonstrate which population and market characteristics in‡uence the
cost of search. Of …rst note in Table 5 is positive relationship between population mean income and
search costs. Across all speci…cations, the mean income in a market positively a¤ects the mean of
the consumer search cost distribution, and is statistically highly signi…cant. In terms of magnitude,
a 10% ($6; 410) increase in household income increases the expected search costs by $0:071 per
gallon. Furthermore, the standard deviation of household income within a market positively a¤ects
the standard deviation of the search costs in a market. These …ndings tightly link the market
income and search cost distributions. Appendix Table A5 presents results when wholesale data are
not incorporated into the estimation, and therefore variation in retail prices rather than markups
are used to identify the model. The income results are robust to this alternative speci…cation,
and income estimates are the only results that are robust to estimating the model with prices or
markups. The results are also robust to di¤erent measures of household income, such as the median
and median absolute deviation of income.
To get a better sense of the extent to which household income and other demographics explain
variation in the mean and standard deviation of search cost distributions across markets, we regress
the predicted market-level search cost mean and standard deviation on demographics. Columns 1
and 5 in Appendix Table A6 demonstrate that the household income mean and standard deviation
explain about 63% and 57% of the variation in the mean and standard deviation, respectively.
The positive relationship between the distribution of search costs and income suggests that
information acquisition costs are an important component of search costs. First, income is likely
to be positively correlated with the opportunity cost of time, and therefore increases the timeinvestment cost of search. Furthermore, people with higher income may have a lower marginal
utility of wealth and thereby gain less utility from saving money on gasoline. It follows that higher
income consumers may have a lower incentive to spend time searching for a lower price, which
supports the information cost interpretation.
Meanwhile, we do not …nd as much support for information processing as a major source of
search costs. Mean years of education is not signi…cant in any of the speci…cations, and the standard deviation of education only enters signi…cantly at the 10% level when a normal distribution
is …tted and wholesale costs are not included. It seems reasonable to expect consumers with a
higher education to have lower information processing costs, yet the regressions do not produce
this …nding. There is modest support for older populations having a lower cost of search, as we
19
estimate a negative relationship between mean age and mean search costs at the 5% or 10% level
in some speci…cations (although not the baseline). It may be that older consumers, with more
shopping experience and a better understanding of road patterns, all else equal, have lower information processing costs; however, this interpretation of age is somewhat speculative. In general,
it may not be possible to strictly separate demographics and market characteristics into either
information acquisition cost or information processing categories. Accordingly, we do not rule out
the information processing interpretation of search cost.
Table 5 does contain results that may not …t with either story. The average distance between
stations is found to negatively relate to the mean of the search cost distribution. This …nding seems
to contradict consumers engaging in costly search by driving between stations. However, if stations
endogenously locate close together in markets where demand is mostly met by travelers with high
search costs, perhaps near interstate highway exits, a negative relationship between mean distance
and search costs may arise. This …nding, however, is not robust to estimating the model using price
data rather than markups. Similarly, we …nd a negative relationship between the standard deviation
of age and the standard deviation of search costs when estimating the model with markups, but
not prices. We see no direct relationship between this …nding and either potential determinant of
search costs.
Finally, the results in this section provide a rationale for time-invariant demand-side characteristics, such as income and age, a¤ecting intertemporal price dispersion. While these variables are
widely recognized to impact cross-market price dispersion, we show that they can also indirectly
a¤ect price changes over time through their impact on the distribution of search costs.10
Overall, in this section, we document the heterogeneity in search cost distribution across markets. In the following section, we analyze, through simulation, how exogenous changes in the search
cost distribution a¤ect equilibrium prices.
7
Policy Experiments: A Reduction in the Costs of Search
This section adopts the search cost distribution parameter estimates from column 1 of Table 5 to
perform “what-if”experiments that quantify the e¤ect of changes in search costs on equilibrium
prices and consumer search behavior. We analyze a policy that simultaneously reduces the mean
and variance of the search cost distribution, and the unique impact within each of the 366 markets
included in the stage 2 regressions. Many policies aimed at reducing consumer search costs will
reduce both the mean and variance of search costs in a market. For example, a regulation requiring
gas stations to post prices on a website may decrease search costs for consumers at the high end of
the distribution, but leave unchanged search costs for consumers at the low end that may already
be using a similar website, such as gasbuddy.com. Similarly, a policy that requires gas stations
to clearly post the price for customers paying with cash or credit may reduce both the mean and
10
We thank the Associate Editor for this observation. Appendix A2 provides empirical evidence that demand-side
characteristics do not directly in‡uence intertemporal price dispersion outside the scope of our model.
20
variance of the search cost distribution, as it may lower the cost of search for credit card consumers
and leave unchanged the cost for cash customers.
The policy decreasing both the mean and standard deviation of the search cost distribution can
either increase or decrease the expected price. The intuition is as follows. Lowering the mean of the
search cost distribution, all else equal, leads to more intense search and lower prices. Conversely,
decreasing the variance of the search cost distribution, all else equal, leads to less search and higher
prices. The reason for higher prices when search costs become less heterogeneous is that …rms
face a trade-o¤ between setting a low price and selling to all consumers and setting a high price
and selling to only consumers with low search intensity. When search costs become su¢ ciently
homogeneous the trade-o¤ always favors setting the highest price, as the sales from relatively lower
search cost consumers becomes too small. The incentive to only set a high price may remain even
if the average cost of search decreases. In Appendix A1, we closely examine the impact of lowering
the mean and/or variance of the search cost distribution within a hypothetical market of average
demographic characteristics.
For the policy counterfactuals, we consider a situation in which consumers’search costs become
less heterogeneous (but not completely homogeneous) and the expected search costs decrease, which
R
we de…ne as c dFc . We conduct the policy experiment by reducing the standard deviation by
10% and the expected value of search costs by 20% separately for each of the 366 isolated markets.
A 20% decrease in the expected value of search costs for a market with average demographics is
equivalent to a 26% (or $17; 164) reduction in the household income. To perform the experiments,
we …rst recover the mean and variance of the search cost distribution for each market by using
the second-stage estimates and pertinent demographic variables. We then solve for the equilibrium
…rm price distribution and consumers search behavior using the structural model. Because there
may be multiple price dispersion equilibria, we try 10 unique starting values for a given market.
[Insert Figures 6a and 6b about here.]
Figure 6a summarizes the changes in the mean price in each market. The distribution is
bimodal with the two modes falling on opposite sides of zero. Furthermore, the distribution exhibits
heterogeneity in both the direction and magnitude of changes across markets. In left hump of the
distribution, the new price dispersion equilibria are characterized by an average price decrease due
to a lower expected cost of search and an increased number of searches. In the right hump, however,
there are higher average prices; these are markets in which the price dispersion equilibrium vanishes,
and only the monopoly equilibrium remains. The distribution is skewed to the right, illustrating
that the magnitude of the positive price changes are, on average, larger than the negative changes.
Indeed, the average price change across markets is positive and $0:051. To con…rm the …nding,
Figure 6b presents the changes in average prices when we reduce the standard deviation by 20%,
while maintaining a 20% reduction in mean search costs. As expected, there are even more markets
with higher prices, and the average price change across markets increases to $0:088.
In summary, we show a reduction in the mean of the search cost distribution coupled with a lower
variance may result in higher average prices for a non-negligible number of markets. Therefore, a
21
well intentioned policy aimed at decreasing the cost of search may unintentionally lead to higher
prices for consumers and pro…ts for …rms.
8
Conclusions
We document signi…cant variation in the distribution of consumer search costs across geographical
markets for retail gasoline, and explain the variation using observable demographics and market
characteristics. Based on a …xed-sample search model and daily price data, we recover the distribution of search costs for a set of geographically isolated markets. The empirical approach extends
the existing …xed-sample search models by (1) incorporating wholesale prices and demographics
and (2) utilizing multiple geographic markets. We …nd that the distribution of income explains the
shape of the search cost distribution, suggesting that opportunity costs are an important driver of
consumers’search costs. Our results also provide a rationale for how time-invariant characteristics
at the market level, such as consumer income, may contribute to intertemporal price variation.
We use the estimated search costs in each market to conduct counterfactual policy experiments
that examine the impact of changing the mean and variance of the search cost distribution. The
counterfactual simulations for 366 geographic markets con…rm that subtle changes to the shape of
the search cost distribution can have a large impact on …rm prices and consumer welfare, and the
e¤ect of the policy can vary widely across markets. In some markets, policy that reduces the mean
and variance of search costs may have the unintended consequence of reducing consumer welfare.
The empirical and counterfactual results have two managerial implications for a …rm entering
a new geographic market. First, perhaps counterintuitively, entering a market with uniformly low
income might yield higher pro…t margins than entering a market with high and dispersed income.
Second, an entrant may want to calculate the expected pro…ts of entry, and understanding how
demographics a¤ect search cost distributions, and therefore pricing, allows …rms to more precisely
project revenues. The …ndings suggest a list of demographic variables, such as income and age, that
may help predict the cost of consumer search when …rms are formulating their pricing strategies.
22
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26
Figure 1a
Example of 1.5-Mile Radius Isolated Markets at Capemay, New Jersey
Market 1
Market 3
Market 2
Note: A small red circle represents a gas station location. A large black circle has a 1.5-mile radius.
Different terrain colors represent different census tracts. Out of Markets 1, 2, and 3 with more than one
station, only Market 1 qualifies as an "isolated" market in our sample, because (1) every station is located
within 1.5 miles of all other stations and (2) every gas station in the market belongs to the same census
tract (Rio Grande for Market 1).
Figure 1b
Distribution of Number of Stations by Isolated Markets (1.5 Miles Radius, 2007)
200
180
160
Number of markets
140
120
100
80
60
40
20
0
2
3
4
5
6
Number of stations
27
7
8
9
11
Figure 2a
Notes: The first panel is the distribution of prices across all isolated markets from February 27th to March 28th, 2007.
The remaining panels are the distribution of prices over the same time in three sample isolated markets with three gas
stations.
Figure 2b
Notes: The first panel is the distribution of markups across all markets from February 27th to March 28th, 2007. The
remaining panels are the distribution of markups in three sample isolated markets with three gas station, and are the
same markets as in Figure 2a.
28
Figure 3a
Histograms of Average Market Prices and Standard Deviation of Prices
Figure 3b
Scatterplot of Standard Deviation of Prices and Average Market Prices
Notes: The average market price has a state fixed effect removed. This largely controls for state taxes.
The standard deviation is measured using all oberved station prices in an isolated market for the 30-day
window. We use data from the 367 isolated markets used in the markup specification.
29
Figure 4a
Estimated Search-Cost CDF from Five Randomly Picked Markets, February 27 through March 28, 2007
Note: The horizontal axis is the search cost in dollar per gallon. This figure plots the combination of estimated ⊿i
and Fc(⊿i) for each of five geographically isolated markets in Texas. All markets have three stations. For a given
market, the right and left points correspond to (⊿1 , Fc(⊿1)) and (⊿2 , Fc(⊿2)), respectively.
Figure 4b
Empirical and Estimated (dash) Price Distribution, February 27th through March 28th, 2007
Note: A market in Florida. The horizontal axis is retail price per gallon.
30
Figure 5a
Histograms of Mean of Estimated Search Cost Distribution
Figure 5b
Histograms of Standard Deviation of Estimated Search Cost Distribution
31
Figure 6a
Change in Average Price after a 20% Decrease in Expected Value and 10% Decrease in Standard Deviation of Search
Costs
Figure 6b
Change in Average Price after a 20% Decrease in Expected Value and 15% Decrease in Standard Deviation of Search
Costs
32
Table 1
Summary Statistics for Demographics across Isolated and Non-Isolated Geographical Markets
Mean
Std dev
Minimum
Maximum
Mean household income ($)
64,163
27,577
24,328
228,277
Years of education
12.625
1.158
8.643
15.761
Age
39.082
5.092
26.489
63.020
Distance between stations (miles)
0.433
0.339
0.002
1.476
Standard deviation of income
48,168
13,190
18,428
117,873
Mean household income ($)
70,608
32,907
11,306
396,574
Years of education
13.053
1.336
7.592
17.368
Age
37.177
5.525
17.602
77.193
Distance between stations (miles)
0.862
0.213
0.002
1.498
Standard deviation of income
50,085
16,137
6,822
263,025
Isolated Markets
Non-Isolated Markets
Note: The data source is the 2006-2010 American Community Survey. The first set of summary statistics are for
isolated markets, as defined in the second section; 367 isolated markets exist. The second set of statistics are for
all markets that do not fit the isolated market critieria; 37,746 "non-isolated" markets exist. A firm can belong to
more than one "non-isolated" market, because a market is defined as a 1.5-mile radius around each firm in the
data; therefore, many overlapping markets exist. When the set of "non-isolated" markets is restricted such that
each firm can belong to only one market, the summary statistics are largely unchanged; 5,138 of these "nonoverlapping/non-isolated" markets exist.
33
Table 2
Price Dispersion Summary Statistics
All Prices
Average Across Isolated Markets
Retail Price
Markup
Retail Price
Markup
Minimum
2.549
0.229
2.964
0.630
(0.101)
(0.082)
Maximum
3.549
1.232
Mean
3.127
0.764
Range (= Max - Min)
1.000
1.003
Standard deviation
0.099
0.089
3.226
(0.085)
3.124
(0.070)
0.262
(0.105)
0.067
(0.033)
354
0.859
(0.085)
0.761
(0.061)
0.229
(0.026)
0.057
(0.102)
367
Number of markets
Note: The above statistics are for regular-grade gasoline prices from isolated markets in the states
of CA, FL, NJ, and TX from February 27 through March 28, 2007. Markup is defined as the retail
regular fuel price minus the wholesale cost. The first two columns present statistics when price
observations are pooled across all isolated markets. There are a total of 12,250 price observations
across all isolated markets. The last two columns give the average of the statistics across all
isolated markets, and standard deviations are in parenthesis. For example, the minimum observed
price in any isolated market is $2.549, and the average minimum price across all isolated markets
is $2.964.
34
Dispersion measure
(1)
Mean income
Mean years of education
Mean age
Mean distance among stations
Standard devation of income
Standard devation of education
Standard devation of age
0.068
(0.044)
-0.012
(0.008)
-0.001
(0.001)
0.007
(0.013)
-0.070
(0.090)
0.025
(0.017)
0.000
(0.003)
Number of firms
Table 3
Price Dispersion Regression Estimates
Sample range
Sample standard devation
(2)
(3)
(4)
(5)
(6)
(7)
0.091**
(0.043)
-0.010
(0.008)
-0.000
(0.001)
0.000
(0.013)
-0.116
(0.088)
0.008
(0.017)
-0.003
(0.003)
0.018***
(0.003)
Log of mean income
Log of mean years of education
Log of mean age
Log of mean distance among stations
Log of standard devation of income
Log of standard devation of education
Log of standard deviation of age
Constant
0.323**
(0.129)
0.350***
(0.123)
0.011
(0.012)
-0.003
(0.002)
0.000
(0.000)
-0.005
(0.003)
-0.009
(0.025)
0.007
(0.005)
-0.001
(0.001)
0.067*
(0.038)
-0.176*
(0.102)
-0.041
(0.044)
0.007*
(0.004)
-0.048
(0.049)
0.059
(0.048)
0.027
(0.075)
0.457
(0.294)
0.018***
(0.003)
0.077**
(0.037)
-0.123
(0.101)
-0.015
(0.043)
0.002
(0.004)
-0.070
(0.049)
0.024
(0.047)
-0.043
(0.075)
0.568**
(0.287)
0.082**
(0.036)
0.015
(0.012)
-0.003
(0.002)
0.000
(0.000)
-0.006*
(0.003)
-0.016
(0.025)
0.004
(0.005)
-0.001
(0.001)
0.003***
(0.001)
0.086**
(0.036)
0.015
(0.010)
-0.046
(0.030)
-0.001
(0.011)
0.000
(0.001)
-0.010
(0.012)
0.017
(0.013)
-0.008
(0.019)
0.122
(0.086)
Observations
367
367
367
367
367
367
367
Notes: The sample range is defined as the difference between the maximum and minimum observed price
from February 27th to March 28th, 2007 in an isolated market. The standard deviation is defined as the sample standard
deviation of all observed prices in a market over the same date range.
Robust standard errors are in parentheses. Income is standardized to $100,000
*** p<0.01, ** p<0.05, * p<0.1
35
(8)
0.003**
(0.001)
0.016
(0.010)
-0.038
(0.030)
0.003
(0.011)
-0.000
(0.001)
-0.013
(0.013)
0.012
(0.014)
-0.019
(0.020)
0.140
(0.086)
367
Table 4
Estimated Search-Cost CDF for All Markets
Mean
Std. Dev
Min
Max
0.664
0.301
0.063
0.073
0.107
0.105
0.100
0.064
0.098
0.000
0.166
0.155
0.130
0.112
0.095
0.139
0.089
0.152
0.060
0.138
.
.
0.004
0.031
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.166
0.936
0.755
0.781
0.396
0.682
0.273
0.512
0.124
0.195
0.000
0.166
367
367
367
180
117
64
30
11
5
2
1
Marginal expected savings from searching l+1 versus l stations (Δ l )
Δ1
0.032
0.014
Δ2
0.016
0.008
Δ3
0.010
0.005
Δ4
0.007
0.003
Δ5
0.005
0.002
Δ6
0.004
0.002
Δ7
0.003
0.001
Δ8
0.002
0.001
Δ9
0.002
.
Δ10
0.002
.
0.007
0.001
0.000
0.000
0.003
0.002
0.002
0.002
0.002
0.002
0.100
0.044
0.026
0.016
0.011
0.007
0.003
0.003
0.002
0.002
367
180
117
64
30
11
5
2
1
1
Valuation-cost margin ($ per gallon)
0.995
0.000
367
Proportion of people with l price quotes (q l )
q1
q2
q3
q4
q5
q6
q7
q8
q9
q10
q11
0.261
0.217
# of Obs.
Note: The estimated valuation-cost margin measures the gap between the utility and the marginal cost of
providing gasoline per gallon (i.e., x = v j - r j ) for each market. This valuation-cost margin measures the
maximum profit margin per gallon possible from that market.
36
Table 5
Nonlinear Least Square Estimation of Search-Cost Cumulative Distribution using Markup Price
Markup price
Price
Lognormal
Distributional assumption
Normal
(1)
(2)
(3)
(4)
-6.926***
(1.980)
0.716***
(0.175)
-0.361
(0.962)
-0.572
(0.510)
-0.594***
(0.214)
-5.838***
(1.905)
0.609***
(0.118)
-5.647***
(1.733)
0.408**
(0.195)
-0.390
(0.690)
-0.019
(0.088)
0.0196***
(0.007)
-0.002
(0.034)
-0.030*
(0.018)
-0.0155**
(0.008)
-0.014
(2.590)
0.502***
(0.123)
-0.284
(0.326)
-1.392**
(0.571)
0.011
(2.631)
0.499***
(0.124)
-1.492***
(0.561)
17.331
726
Mean of distribution
Constant
Mean income
Mean years of education
Mean age
Mean distance among stations
-0.797**
(0.392)
-0.596***
(0.213)
-0.5685***
(0.201)
Standard deviation of distribution
Constant
Standard deviation of income
Standard deviation of years of education
Standard deviation of age
Mean squared error
Number of observations
-2.656**
(1.183)
0.351***
(0.110)
-0.420
(0.320)
-0.948
(2.585)
0.398**
(0.163)
-0.460
(0.370)
-1.768**
(0.724)
17.372
17.489
18.446
726
726
726
Note: Standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1. The regressors are in logs.
37